Alister,
I've never heard of any such restriction. Nothing I can find anywhere in the SCHSL rules to support that, and I don't think anyone would want to play in an early tournament if that was the case. Everything I read points to any date prior to March 7 being open for scrimmages, regardless of tournaments.
Tournament games only count on the record for playoff seeding as a third-tier tiebreaker...if region records are tied, then you go head-to-head; if that is tied, then to overall records excluding tournaments; only if THAT record is tied do you count total record including tournament matches, and even that is a region rule, not a state rule. Wouldn't make sense to say that you can't scrimmage after a tournament because those games "count;" they are not regular season games and you are still in scrimmage territory. Sounds like someone just doesn't want you tearing up the field.